Abstract

A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient-plasticity and grain-boundary theory of Gurtin (2008) is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimisation form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterise the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of three-dimensional numerical examples serve to elucidate the theory.

Item Type:

Articles

Additional Information:

DG and PW like to acknowledge the support of the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG) provided for the international research training group GRK 1627. BDR acknowledges the support provided by the National Research Foundation through the South African Research Chair in Computational Mechanics. Part of this work was completed while BDR was visiting the Institute of Continuum Mechanics (IKM), Leibniz Universität Hannover, as the recipient of a Georg Forster Research Award from the Alexander von Humboldt Foundation. The hospitality and funding provided by these organizations are acknowledged with thanks.